When constructing a perpendicular bisector, the compass opening must be greater than half the length of the segment because it ensures that the two arcs drawn from the endpoints of the segment intersect each other properly.
To construct a perpendicular bisector, you first need to draw two equal arcs which intersect each other. These arcs are drawn from the endpoints of the original segment. The radius of these arcs is set using a compass, and it should be greater than half the length of the segment.
If the compass opening is exactly half the length of the segment, the arcs drawn from the endpoints will not intersect each other. As a result, the perpendicular bisector cannot be properly constructed. By having a compass opening greater than half the length of the segment, the arcs will intersect each other, allowing for the accurate construction of the perpendicular bisector.
When constructing a perpendicular bisector, why must the compass opening be greater than 1/2 the length of the segment?
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